Psychometricians have long been aware that many differences-of-degree often mask underlying differences-of-kind (Michell, 2011). A difference-in-kind within a measure of a concept means that different values have different causal properties. Differences-of-degrees relate to increases or decreases in the magnitude of a given causal property.
This Paper explores whether concepts that include differences-of-degree are actually compatible with set-theory based within-case methods (Mahoney and Goertz, 2012; Blatter and Haverland, 2012; Beach and Rohlfing, 2015). Within-case analysis builds on the ontological assumption of asymmetry (i.e. set relations), where we assess causal claims in the form of causal condition C being linked to outcome O through an explicitly theorized causal process (mechanism, M).
In this Paper, I contend that degree differences in concepts are at best irrelevant when asessing within-case (mechanistic) evidence because we are attempting to trace empirically the operation of a causal mechanism (or set of mechanisms) within a case. Indeed, if there is variation then we are no longer tracing the mechanism in the same case! Even more problematic, given the sensitivity of mechanisms to contextual factors, there is the risk that conceptualizations of causes and outcomes that include degree differences will actually mask kind-differences that would change the causal character of the operation of the process. Therefore, operating with concepts that include degree-differences when inferring from mechanistic evidence from the single case to the rest of the population creates a very serious threat of making flawed inferences because the population to be inferred to is causally heterogeneous, as kind-differences that are masked behind degree-differences. I contend that operating with fuzzy-set scores and lexical scales does not solve the problem. Instead, when engaging in detailed case studies, we should only operate with concepts measured using differences-of-kind; everything else is either irrelevant or raises the serious risk of producing flawed generalizations.
